Answer:
The work done against friction is 372 joules
Explanation:
It is given that,
Mass of block, m = 24 kg
Radius of the track, r = 15 m
Acceleration due to gravity, [tex]a=9.8\ m/s^2[/tex]
If the kinetic energy of the block at the bottom of the track is, 3900 J
Let P is the work done against friction. It is given by :
[tex]P=mgh[/tex]
Here, h = r
[tex]P=24\ kg\times 9.8\ m/s^2\times 15\ m[/tex]
P = 3528 J
Since it ends up with 3900 J, the work done is given by or the lost in energy will be :
W = 3900 - 3528
W = 372 joules
So, the work done against friction is 372 joules. Hence, this is the required solution.
Technician A says that the aspect ratio of a tire represents the relationship between the tire's cross-sectional height to its cross-sectional width. Technician B says that low aspect ratios provide a softer ride because they will deflect more over irregular surfaces and under heavy loads. Who is correct?
a. Technician A
b. Technician B
c. Both A and B
d. Neither A nor B
Answer:
Technician A
Explanation:
Often referred to as the profile or series, the aspect ratio of a tire is determined by dividing a tire’s section height by its section width when the tire is: inflated to maximum air pressure, mounted on the approved measuring rim, and under no load. This rules out Technician B.
A tire with a lower aspect ratio responds to lateral force more effectively than a tire with a higher aspect ratio. The aspect ratio affects steering stability. Generally, the shorter the sidewall, or the lower the aspect ratio, the less time it takes to transmit the steering input from the wheel to the tread. The result is quicker steering response. Aspect ratio also affects the tread contact patch. As a rule, a low-profile tire produces a wider tread contact patch. This wider tread contact patch creates a stiffer footprint that reduces distortion and provides improved cornering traction. Aspect ratio also impacts ride. A low-profile tire usually has a stiffer ride than the standard aspect ratio of 75 or more.
Final answer:
A. Technician A is correct about the aspect ratio of a tyre, while Technician B is incorrect about the impact of low aspect ratios on ride softness.
Explanation:
Technician A is correct. The aspect ratio of a tyre indeed represents the relationship between the tyre's cross-sectional height to its cross-sectional width. The aspect ratio is a critical factor in determining the tyre's performance and characteristics. Technician B is incorrect. Low aspect ratios do not provide a softer ride because they will deflect more over irregular surfaces.
In the given case, the aspect ratio primarily affects the tyre's handling, stability, and sidewall height. In conclusion, Technician A provides an accurate explanation regarding the aspect ratio of a tyre in relation to its dimensions and characteristics.
A body of mass 400 kg is suspended at a lower end of a light vertical chain and is being pulled up vertically. Initially the body is at rest and the pull on the chain is 6000 g (g is 9.8 m/s^2) The pull gets smaller uniformly at the rate of 360g N per each meter through which the body is raised. What is the velocity of the body when it has been raised 10m?
Answer:31.62 m/s
Explanation:
Given
mass of body [tex]m=400 kg[/tex]
Pull on chain is [tex]F_1=6000g N=60 kN[/tex]
Pull get smaller at the rate of [tex]F_2=360g N/m[/tex]
Net Upward Force [tex]F=6000 g-360 g\times 10=24 kN[/tex]
net acceleration [tex]a=\frac{F}{m}[/tex]
[tex]a=\frac{24\times 1000}{m}[/tex]
[tex]a=\frac{24000}{400}[/tex]
[tex]a=60 m/s^2[/tex]
but g is acting downward
[tex]a_{net}=a-g=60-10=50 m/s^2[/tex]
using [tex]v^2-u^2=2 as[/tex]
here initial velocity is zero
[tex]v^2=2\times 50\times 10[/tex]
[tex]v=31.62 m/s[/tex]
The velocity of the body will be "31.62 m/s".
Given:
Mass of body,
m = 400 kgPull on chain,
[tex]F_1= 6000 \ g.N[/tex][tex]F_2 = 360 \ g.N/m[/tex]The net upward force will be:
→ [tex]F = 6000-360\times 10[/tex]
[tex]= 6000-3600[/tex]
[tex]= 2400[/tex]
or,
[tex]= 24 \ kN[/tex]
Now,
The net acceleration will be:
→ [tex]a = \frac{F}{m}[/tex]
[tex]= \frac{24\times 1000}{400}[/tex]
[tex]= 60 \ m/s^2[/tex]
But,
"g" is acting downwards then,
→ [tex]a_{net} = a -g[/tex]
[tex]= 60-10[/tex]
[tex]= 50 \ m/s^2[/tex]
By using,
→ [tex]v^2-u^2=2as[/tex]
[tex]v^2= 2\times 50\times 10[/tex]
[tex]= 1000[/tex]
[tex]v = \sqrt{1000}[/tex]
[tex]= 31.62 \ m/s[/tex]
Thus the above answer is right.
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Which two security measures must an engineer follow when implementing layer 2 and layer 3 network design?
Answer:
Utilize the Private VLAN feature to segregate network traffic at Layer 2, and
Utilize the ARP inspection feature to help prevent the misuse of gARP.
Explanation:
An Engineer designing layer 2 and layer 3 network, must Utilize the Private VLAN feature to segregate network traffic at Layer 2 and Utilize the ARP inspection feature to help prevent the misuse of gARP.
An astronaut drops a ball off the edge of a crater on the Moon, where gravity is 1.6 m/s(s). If it takes 5 seconds for the ball to reach the bottom of the crater, what is the depth of the crater? (Need HELP, AAAAAAAAAAAAAAAAAAAAAA.)
Answer:
The depth of the crater is 20[m]
Explanation:
We can solve this problem using the kinematics equations, it should be noted that the negative sign of acceleration means that the drop of the object is down.
Data:
a = 1.6[m/s^2]
t = 5 [s]
[tex]y=y_{0} +v_{0} *t-\frac{1}{2} *g*(t)^{2}[/tex]
v0= 0, because there is not initial veocity
y = final distance = 0 the bottom of the crater
g = a = acceleration of the crater [m/s^2]
y0= Point where the ball was dropped. = Distance from the original point to the bottom of the crater.
[tex]y_{0} =\frac{1}{2}*1.6*(5)^{2}\\ y_{0} = 20 [m][/tex]
Earl is using his hands to hold a metal pan 10 centimeters above a hot burner. How can this scenario be changed to demonstrate conduction between the pan and the burner?
Answer:
Earl needs to touch the pan to the burner.
Explanation:
Earl is demonstrating heat transfer by conduction.
Conduction is the transition of heat energy by direct contact. Hotter molecules have more momentum and they move faster.These hot molecules collide with the cooler ones, transfer their energy to cooler particles , this process is continued to pass it on to other molecule near to them.
Earl needs to touch the pan to the burner.
Answer:
D the answer is D
Explanation:
When following a motorcycle, drivers must remember that motorcycles can ____________ than other vehicles.
Answer:
Stooping more Quickly
Explanation: Stooping more quickly means that Motor cycles can easily bend and stop,this is due to it's design, Motor cycle have only two wheels,they contain just two tyres one in front and one at the back,they are not as firm on the ground when compared to other vehicles such Motor car. They have a lower weight which makes them easily bent or stopped once there's any barrier.
Motorcycles can stop quicker than other vehicles.
Explanation:When following a motorcycle, drivers must remember that motorcycles can stop quicker than other vehicles. Due to their smaller size and weight, motorcycles have a shorter stopping distance. This means that drivers should maintain a safe following distance to avoid rear-ending the motorcycle.
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How will W change if the initial speed of the box at Point A is increased by a factor of 2?
If the initial speed of the box at Point A is increased by a factor of 2, the final velocity, denoted as W, will also increase by a factor of 2.
Explanation:If the initial speed of the box at Point A is increased by a factor of 2, the final velocity of the box, denoted as W, will also increase by a factor of 2.
For example, if the initial speed of the box was 10 m/s, after increasing it by a factor of 2, the new speed would be 20 m/s.
Therefore, option (a), It will increase by a factor of two, is the correct answer choice.
When a sound wave travels directly toward a hard wall, the incoming and reflected waves can combine to produce a standing wave. There is an antinode right at the wall, just as at the end of a closed tube, so the sound near the wall is loud. You are standing beside a brick wall listening to a 80Hz tone from a distant loudspeaker.
How far from the wall must you move to find the first quiet spot? Assume a sound speed of 340 m/s.
Answer:
L= 1.06 m
Explanation:
frequency of a wave in a pipe closed at one end is given by
[tex]f= \frac{v}{4L}[/tex]
L= length of the pipe
v= velocity of wave
therefore, the length of the pipe
[tex]L= \frac{v}{4f}[/tex]
[tex]L= \frac{340}{4\times80}[/tex]
L= 1.06 m
L= 1.06 m far from the wall must you move to find the first quiet spot.
The distance from the wall(i.e the pipe length) you need to move to find the first quiet spot is 1.06 m.
What is the frequency of a sound wave in a closed pipe?The smallest standing wave pattern, i.e the first fundamental frequency or harmonic for a closed pipe usually consists of one node and an antinode. When the wavelength of a closed pipe of length L is 4 L, the basic standing wave is formed.
The frequency of a sound wave for a closed pipe at one end may thus be represented using the following formula:
[tex]\mathbf{f = \dfrac{v}{4L}}[/tex]
where;
L = pipe length = ???v = velocity of the wave = 340 m/sf = frequency = 80 HzThus, the length of the pipe can be computed as:
[tex]\mathbf{L = \dfrac{340 \ m/s}{4\times 80 \ Hz}}[/tex]
L = 1.06 m
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The driver must stop and remain stopped to let a pedestrian cross at a crosswalk when the pedestrian is _____________.
A. on the half of the road with traffic going in the opposite direction
B. on the half of the road that the vehicle is traveling
C. anywhere on a two-way street
Answer: the correct option is B ( on the half of the road that the vehicle is traveling).
Explanation: according to Georgia Code About Pedestrians; The driver must stop and remain stopped to let a pedestrian cross at a crosswalk when the pedestrian is
on the half of the road that the vehicle is traveling.
Answer:
B
Explanation:
The driver must stop and remain stopped to let a pedestrian cross at a crosswalk when the pedestrian is _____________.
A. on the half of the road with traffic going in the opposite direction
B. on the half of the road that the vehicle is traveling
C. anywhere on a two-way street
According to the law regrading pedestrian, the pedestrian has the right of way immediately she is crossing on the crosswalk and is half of the road that the vehicle is travelling.
These rules are there for the safety of the driver, pedestrians and other road users
Which wavelengths of light drive the highest rates of photosynthesis?
Answer:
400-450 nm and 670-680 nm
Explanation:
Which wavelengths of light drive the highest rates of photosynthesis?
400-450 nm and 670-680 nm
Light in the violet-blue and red portions of the spectrum is most effective in driving photosynthesis
photosynthesis is the process through which green plant manufacture there food through sunlight, they synthesize nutrient in the this process through chlorophyll thereby releasing oxygen as a bye-product. a spectrum contains 7 colours combined . the violet-blue and red portions of the spectrum is most effective
What is the difference between balanced and unbalanced forces
Balanced forces are equal and opposite, causing no change in an object's movement, leading to static equilibrium. On the contrary, unbalanced forces change an object's velocity or direction, causing it to move or accelerate.
Explanation:The primary difference between balanced and unbalanced forces lies in their effects on the motion of an object. Balanced forces are equal and opposite forces that act on an object, resulting in no change in its velocity or direction. An example would be a static car or an ice hockey stick lying flat with two equal and opposite forces applied to it. Friction is negligible and the gravitational force is balanced by the support, leading to static equilibrium.
On the other hand, unbalanced forces are not equaled.
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Why are summer days longer than winter days on earth?
Answer:
Tilt of the Earth
Explanation:
The Earth's rotational axis is titled at an angle 23.4°. When then northern hemisphere is pointed towards the Sun it is summer in the northern hemisphere and winter in the southern hemisphere.
In the northern hemisphere a day would be longer and gets more sunlight than the southern hemisphere.
The same happens when it is summer in the southern hemisphere.
Answer:
The sun is father away during the winter.
Explanation:
In the northern hemisphere, during the winter it is summer in the southern hemisphere. The sun is farther away for us so the days get shorter in the winter since the sun inches away faster.
Let v⃗ A be the velocity of the car at point A. What can you say about the acceleration of the car at that point?
Answer and Explanation:
Let the velocity of the car at a point is A is v
We have to tell about the acceleration at that point
Acceleration at that point will be perpendicular to the velocity and directed inside of the track
We can tell anything about the magnitude of the acceleration as magnitude of acceleration is the rate of change of velocity and here we have no information about time
While a car's velocity at a given point only describes its speed and direction at that moment, its acceleration at that point accounts for changes in speed and direction over time. To ascertain acceleration at a point, the velocities before and after that point need to be compared.
Explanation:The velocity of a car at a given point, such as point A, tells us it's direction and speed at that instant. However, the acceleration of the car at that point is a different matter. Acceleration is defined as the change in velocity per unit time, and it doesn't only involve speed, but also direction. A car could be moving at a constant speed, but if it's changing direction, it's considered to be accelerating. Therefore, to ascertain acceleration at point A, we would need to know not just the velocity at point A, but also at points immediately before and after.
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A 2.0-kilogram laboratory cart is sliding across a horizontal frictionless surface at a constant velocity of 4.0 meters per second east. What will be the cart's velocity after a 6.0-newton westward force acts on it for 2.0 seconds and in what direction?
Answer:
v = 2 m/s (West)
Explanation:
Given
m = 2 Kg
v initial = 4 m/s (East)
F = 6 N (West)
t = 2 s
We can use the formula
v = v initial + a*t
if F = m*a ⇒ a = F/m = 6 N / 2 Kg
a = 3 m/s² (West)
then
v = v initial + a*t = (4 m/s) + (-3 m/s²)(2 s)
v = - 2 m/s = 2 m/s (West)
The velocity is a vector quantity. The velocity of the given cart is 2 m/s to the west.
To solve the given problem, use the kinematic equation,
[tex]v = s + at[/tex]........................1
Where,
[tex]s[/tex] - initial speed = 4 m/s
[tex]a[/tex] - acceleration
[tex]t[/tex] - time - 2 s
Acceleration can be calculated by the formula,
[tex]F = ma[/tex] or
[tex]a = \dfrac Fm[/tex]
Where,
m = mass = 2 Kg
F = force = 6 N
So,
[tex]a = \dfrac {6}2\\\\a = 3\rm \ m/s^2[/tex]
Put the values in equation 1,
[tex]v = 4 +3\times 2\\\\v = \bold {2 m/s}[/tex]
Therefore, the velocity of the given cart is 2 m/s.
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How much work will a machine with a power rating of 1.1 × 103 watts do in 2.0 hours?
A. 1.5 × 106 joules
B. 2.1 × 106 joules
C. 4.0 × 106 joules
D. 8.1 × 106 joules
Answer:
D.
Explanation:
8.1X10 to the power of 6 Joules.
Answer:
7.92×10^6Joules
Explanation:
Power is defined as the rate of change in work done. Mathematically, Power = Workdone/Time
Given power = 1.1×10³watts
Time = 2.0hours = 2×60×60
= 7,200seconds
Workdone = power × time
Work done = 1.1×10³×7200
Workdone = 7,920,000Joules
= 7.92×10^6Joules
An electron is accelerqated in the uniform field betwen two parallel charged oplates. The separation of the plates is 1.20 cm
Answer:
The speed of electron is [tex]8.7\times10^{6}\ m/s[/tex]
Explanation:
Given that,
Separation of the plate = 1.20 cm
Suppose the field is [tex]E=1.80\times10^{4}\ N/C[/tex].
If the electron is accelerated from rest near the negative plate and passes through a tiny hole in the positive plate.
What the speed does it leave the hole?
We need to calculate the acceleration
Using formula of electric force
[tex]F = qE[/tex]
[tex]ma=qE[/tex]
[tex]a=\dfrac{qE}{m}[/tex]
We need to calculate the speed of electron
Using equation of motion
[tex]v^2=u^2+2as[/tex]
[tex]v^2=2as[/tex]
Put the value of acceleration in the formula
[tex]v^2=2\times\dfrac{qE}{m}\times s[/tex]
Put the value into the formula
[tex]v^2=2\times\dfrac{1.6\times10^{-19}\times1.80\times10^{4}\times1.20\times10^{-2}}{9.11\times10^{-31}}[/tex]
[tex]v=\sqrt{2\times\dfrac{1.6\times10^{-19}\times1.80\times10^{4}\times1.20\times10^{-2}}{9.11\times10^{-31}}}[/tex]
[tex]v=8.7\times10^{6}\ m/s[/tex]
Hence, The speed of electron is [tex]8.7\times10^{6}\ m/s[/tex]
Which layer of the atmosphere absorbs the most ultraviolet rays
Answer:
The stratosphere
Explanation:
In the lower portion of the stratosphere there is a high concentration of ozone in relation to other parts of the atmosphere. This region is known as the ozone layer. This layer absorbs most of the Sun's ultraviolet radiation, especially ultraviolet B rays, allowing ultraviolet A rays to pass.
Answer:
TROPOSPHERE
Explanation:
A vertical spring has a spring constant of 100 newtons per meter. When an object is attached to the bottom of the spring, the spring changes from its unstretched length of 0.50 meters to a length of 0.65 meters. The magnitude of the weight of the attached object is
a. 1.1N
b. 15N
c. 50N
d. 65N
Answer:
option B
Explanation:
given,
spring constant = k = 100 N/m
distance of unstretched length = 0.5 m
distance after stretched length = 0.65 m
magnitude of weight = ?
We know,
W = K x
x is the displacement
x = 0.65 - 0.5 = 0.15 m
W = K x
W = 100 x 0.15
W = 15 N
Hence, the correct answer is option B
Final answer:
The weight of the attached object is found by multiplying the spring constant (100 N/m) by the stretch in the spring (0.15 m), which equals 15 N. Therefore, the weight of the object is 15 N.
Explanation:
The weight of the attached object can be calculated using Hooke's Law, which states that the force exerted by the spring (F) is equal to the spring constant (k) multiplied by the displacement from the rest position ( extDelta x): F = k extDelta x. In this case, the spring has a spring constant of 100 newtons per meter and the displacement from the original length of 0.50 meters to the new length of 0.65 meters is 0.15 meters.
Thus, F = 100 N/m exttimes 0.15 m, which gives us a force of 15 N. Since the weight of the object is the force exerted by the spring and these two forces are equal and opposite when the spring is at rest with the object hanging, the weight of the attached object is 15 N. Therefore, the correct answer is (b) 15N.
A person holding weights sits on a spinning stool. Then the person pulls the weights in,decreasing the rotational inertia of the system of the man, the weights,and the stool by a factor of 2. The stool can rotate about its axle with negligible friction.How does the kinetic energy of the system change?
Answer:
Ķ rot = 2K rot
When the arms and weight are retracted toward the body, the energy increases by twice the initial kinetic energy because the moment of inertia has decreased coupled with the energy needed to bring the hands towards the body.
Explanation:
K rot = kinetic energy of system when hands + weight are stretched out = ½ Iw²
Where w = angular velocity when arms and weight are stretched out
I = inertia of the system = ( Ie + Ip) where Ie= moment of inertia of the extra weight carried and Ip = moment of inertia of the person.
Ķ rot = final rotational energy when arms and external weight are pulled in = ½Ìŵ² where Ì =( Ìe + Ìp)
And Ìe = inertia of weight when hands are retracted and Ìp = inertia of person when hand are retracted
Using conservation of angular momentum which is
Iw = Ìŵ
Substitute ŵ = (I/Ì)*W in Ķ rot to give
Ķ rot =½Ì *[ (I/Ì) * W ]²
Ķ rot = ½ ( I²/Ì) * w²
Since K rot = ½ I w²
So Ķ rot = K rot ( I/Ì )...eq3
From the question above system inertia reduces by a factor of 2
Ì = ½I
Sub expression into equ3
Ķ rot = 2K rot
A biker to move from speed of 0 m/s to final speed of 25 m/s in 10 s. What is the acceleration of the bike?
Answer:
a = 2.5 m/s²
Explanation:
given,
initial speed = 0 m/s
final speed = 25 m/s
time = 10 s
acceleration of bike is equal to change in velocity per unit time
[tex]a = \dfrac{\Delta v}{t}[/tex]
[tex]a = \dfrac{v_f-v_i}{t}[/tex]
[tex]a = \dfrac{25-0}{10}[/tex]
a = 2.5 m/s²
hence, acceleration of bike is equal to a = 2.5 m/s²
Unrestrained occupants of a car keep moving during the time the car takes to stop due to ________.
A. centrifugal force
B. gravity
C.inertia
D.precipitation
Answer:
C.inertia
Explanation:
Inertia is a property of matter to maintain its state of motion.
In this case, if the car was moving along with the people in it when the car stopped, the inertia of the people will cause them to continue moving.
This is why in a crash a person can be shot from the car, due to the inertia he has from his previous state of motion.
The complete sentence is: Unrestrained occupants of a car keep moving during the time the car takes to stop due to inertia. (option C)
Unrestrained occupants of a car continue moving forward when the car stops due to inertia, as an object in motion remains in motion unless acted upon by an external force.
Explanation:Unrestrained occupants of a car keep moving during the time the car takes to stop due to inertia. This phenomenon occurs because, according to Newton's first law, an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force. In the context of a car, when it suddenly stops, the passengers inside will continue moving forward because their bodies were initially in motion and there is no forward force directly applied to them to cause a deceleration similar to that of the car.
Centripetal force is the force that causes an object moving in a circular path to move towards the center of the path. However, when the force disappears, inertia is what carries the object in a straight line, tangent to the circular path. While centrifugal force is often used in common language to describe the sensation of being pushed outward in a rotating system, it is not an actual force but rather a perceived effect due to inertia.
An artery is constricted at one location to 1/2 its normal cross-sectional area.
How does the speed of blood past the constriction compare to the speed of blood flow in the rest of the artery? (Note: Assume ideal fluid flow.)
a) it is 1/4 as fast
b) it is 1/2 as fast
c) it is 2 times as fast
d) it is 4 times as fast
Answer:
v₂ = 2 v₁ blood velocity in the built zone is twice the speed of the normal zone, so the correct response is c
Explanation:
For that problem we must use the fluid continuity equation
A₁ v₁ = A₂ v₂
Where point 1 is in the normal artery and point 2 in the contraction
v₂ = v₁ A₁ / A₂
In the exercise indicates
A₂ = ½ A₁
v₂ = 2 v₁
The blood velocity in the built zone is twice the speed of the normal zone, so the correct response is c
An experiment on the earth's magnetic field is being carried out 1.00 m from an electric cable. What is the maximum allowable current int eh cable if the experiment is to be accurate?
The maximum allowable current in the cable for the experiment to be accurate, considering Earth's magnetic field is 0.5 Amps. This is calculated using the magnetic field strength formula and rearranging it to find the current.
Explanation:To answer the question, we would need to use the formula to determine the magnetic field strength generated by a current carrying wire which is B = μ0 * I / 2πr, where B is the magnetic field strength generated by the wire, I is the current, r is the distance from the wire and `μ0` is the permeability of free space which is a constant equal to 4π * 10^-7 T m/A.
Let's rearrange this equation to make I the subject:
I = B * 2πr / μ0
We are told in the question that the maximum magnetic field (B) that does not adversely affect the experiment is 1.0 * 10^-4 T, and the distance (r) is 1.00 m. So substituting these numbers in:
I = 1.0 * 10^-4 T * 2π * 1.00 m / 4π * 10^-7 T m/A
This simplifies to 0.5 A. Therefore, the maximum allowable current in the wire is 0.5 Amps.
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Suppose you have an accounting background and you are considered an expert in the field of discovering errors in electronic spreadsheets. You are considered a knowledge engineer if you are part of a team that is developing an expert system to discover errors in spreadsheets. True or false?
Answer: True
Explanation: A knowledge engineer is a professional who works to improve and builds with the aid of science and also implements advanced logic and AI( artificial intelligence) in computer systems in order to investigate particular issues.
A knowledge engineer also helps tries to emulate the judgements of man.
Since you are part of the team involved in discovering errors in the electronic spread sheet you are a knowledge engineer.
Tarzan steps out of his house and grabs a hanging vine to swing to the ground. If his house is 11.3 m above the ground, what is Tarzan's speed when he reaches the ground?
Answer:
v = 14.88 m / s
Explanation:
For this exercise let's use energy conservation. We place the reference system on the ground
Start. Tarzan before jumping
Em₀ = U = m g h
Final. Upon reaching the ground
[tex]Em_{f}[/tex]= K = ½ m v²
Energy is conserved
Em₀ = [tex]Em_{f}[/tex]
m g h = ½ m v²
v² = 2gh
v = √ 2gh
Let's calculate
v = √ (2 9.8 11.3)
v = 14.88 m / s
A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg·m2. If the arms are pulled in so the moment of inertia decreases to 1.80 kg·m2
Answer:
The angular velocity when the arms are pulled is ω₂= 6.25 rad/s
Explanation:
Assuming that you want to determine the final angular velocity when is the arms are pulled, then it is calculated using the principle of conservation of angular momentum. It states that:
I₁ω₁=I₂ω₂
where I = moment of inertia , ω= angular velocity , 1 and 2 denote the skater with extended hands and pulled respectively.
Thus
I₁ω₁=I₂ω₂
ω₂= I₁ω₁/I₂
replacing values
ω₂= ω₁ *(I₁/I₂) = 5 rad/s *(2.25 kg·m2/1.80 kg·m2) = 6.25 rad/s
ω₂= 6.25 rad/s
Consider a telescope with a small circular aperture of diameter 2.0 centimeters.A) If two point sources of light are being imaged by this telescope, what is the maximum wavelength λ at which the two can be resolved if their angular separation is 3.0×10−5 radians?
Answer:
[tex]4.91803\times 10^{-7}\ m[/tex]
Explanation:
[tex]\theta[/tex] = Angular seperation = [tex]3\times 10^{-5}\ rad[/tex]
[tex]\lambda[/tex] = Wavelength
We have relation
[tex]sin\theta=1.22\dfrac{\lambda}{d}\\\Rightarrow \lambda=\dfrac{dsin\theta}{1.22}\\\Rightarrow \lambda=\dfrac{2\times 10^{-2}sin(3\times 10^{-5})}{1.22}\\\Rightarrow \lambda=4.91803\times 10^{-7}\ m[/tex]
The maximum wavelength of the telescope is [tex]4.91803\times 10^{-7}\ m[/tex]
The maximum wavelength λ at which the two sources can be resolved is of [tex]1.49 \times 10^{-10} \;\rm m[/tex].
Given data:
The diameter of the telescope is, d = 2 cm = 0.02 m.
The angular separation of the two point source of light is, [tex]\theta = 3.0 \times 10^{-5} \;\rm radians = 3.0 \times 10^{-5} \;\rm radians \times \dfrac{\pi}{180}\\\theta = 5.23 \times10^{-7}^{\circ}[/tex].
The angular separation of two point source is also known as apparent distance between the sources, and it is defined as the angle between the two objects as viewed directly by the observer.
The standard relation for the angular separation of telescope is given as,
[tex]sin \theta = 1.22 \times \dfrac{\lambda}{d}[/tex]
here, [tex]\lambda[/tex] is the maximum wavelength of light.
Solving as,
[tex]sin (5.23 \times 10^{-7}) = 1.22 \times \dfrac{\lambda}{0.02}\\\\\lambda = \dfrac{sin (5.23 \times 10^{-7}) \times 0.02}{1.22} \\\\\lambda = 1.49 \times 10^{-10} \;\rm m[/tex]
Thus, we can conclude that the maximum wavelength λ at which the two sources can be resolved is of [tex]1.49 \times 10^{-10} \;\rm m[/tex].
Learn more about the angular separation here:
https://brainly.com/question/14471998
An object is in simple harmonic motion. The rate at which the object oscillates may be described using the period T, the frequency f, and the angular frequency . If the angular frequency decreases, what is the effect on the period and the frequency?
Explanation:
The relation between angular frequency and frequency is directly proportional:
[tex]\omega=2\pi f[/tex]
So, if the angular frequency decreases, the frequency also decreases.
The relation between angular frequency and period is inversely proportional:
[tex]\omega=\frac{2\pi}{T}[/tex]
So, if the angular frequency decreases, the period increases.
When the angular frequency of an object in simple harmonic motion decreases, the period increases and the frequency decreases.
Explanation:When the angular frequency of an object in simple harmonic motion decreases, the effect on the period and frequency is as follows:
a skater increases her speed uniformly from 2.0 m/s to 10 m/s in 3.0s. what is the acceleratioon of the biker?
Answer:
a= 2.667 m/s²
Explanation:
Given that
Initial velocity ,u= 2 m/s
Final velocity ,v= 10 m/s
Time taken ,t= 3 s
As we know that
v = u + at
a=Acceleration ,u=Initial velocity ,v= Final velocity ,t=time
Now by putting the values in the above equation
v = u + at
10 = 2 + a x 3
8 = 3 a
[tex]a=\dfrac{8}{3}\ m/s^2[/tex]
a= 2.667 m/s²
Therefore the acceleration of the biker will be 2.667 m/s²
The total lifetime of the Sun is about 10 billion years, from when it was born to when it dies, and the half-life of 238U is 4.5 billion years. Suppose a particular meteoroid contained 24 micrograms of uranium-238 (238U) when the Sun was born. If the meteoroid is still in orbit when the Sun dies, it will contain _____
Answer:
a little less than 6 micrograms
Explanation:
The half-life of an element is defined as the time in which half of the isotope emits its radiation and becomes a different element. Therefore after 4.5 billion years the meteoroid will contain 12 micrograms of uranium, after 9 billion years will contain 6 micrograms. After 10 billion years will contain a little less than 6 micrograms.